# Thresholds for Bhattacharyya coefficient - when do the distributions differ significantly

Discussion in 'Education' started by Ric, Sep 16, 2020.

1. ### RicGuest

The Bhattacharyya coefficient of two discrete probability distributions is defined as $$BC(p,q) = \sum_{i=1}^n \sqrt{p_iq_i}.$$ This coefficient lies within the interval $[0,1]$ and if $p=q$ then it is 1 as $$\sum_{i=1}^n \sqrt{p_i^2} = \sum_{i=1}^n p_i = 1.$$ Thus values lower than 1 might indicate that $p$ and $q$ differ. Are there any thresholds derived in the literature or significance tests that give guidance when we can accept the hypothesis that $p$ and $q$ differ?